PARAMETRIC METHOD OF SOLVING PROBLEMS OF MATHEMATICAL SAFE ON GRAPHS

Abstract

We consider one method of solving the problem of mathematical safe on certain graphs called parametric. Its gist consist in denoting some variables, corresponding to graph vertices, by certain parameters. Other unknown variables are expressed through these parameters. Then unknown variables chosen in special way are compared and the mentioned parameters are found by solving additional system of equations for these parameters. Dimension of this system is equal to the number of parameters. Solution to the problem i.e. all unknown variables of the original system, are found by solving additional system of equations. In the paper this method is described on specially chosen examples. The method is demonstrated by solving the mathematical safe problem on the graphs of «chain», «ladder» and «window» types that showed its efficiency. Besides special attention is paid to special cases when solution does not exist. This occurs in the cases when the weighed sum of system equations is not divisable without remainder to its modulo. In such cases, to find solution the initial state of the vector b is corrected in such a way that the weighted sum of equations satisfies the above mentioned condition. Then solution of the problem is performed according to the general method scheme.